Weak Acid pH Calculator

Calculate pH of weak acid solutions using the Ka equilibrium expression. Find [H+] by solving x^2/(C-x) = Ka. Includes percent dissociation for any weak acid.

🔬 Acid-Base📐 pH from Ka: x²/(C-x) = Ka🧪 Chemistry
Initial concentration C (mol/L)
Ka of weak acid
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Weak Acid pH Calculator—pH from Ka: x²/(C-x) = KapH

Step-by-Step Examples

Example 1
0.100 M Acetic Acid

Ka(CH3COOH) = 1.8x10^-5.

  • x^2/(0.100-x) = 1.8x10^-5
  • Quadratic: x = 1.34x10^-3 M
  • pH = -log(1.34x10^-3) = 2.87
  • Dissociation: 1.34%
✓ pH = 2.87 (1.34% dissociated)
Example 2
HCN Weak Acid

0.500 M HCN, Ka = 6.2x10^-10.

  • x^2/(0.500-x) = 6.2x10^-10
  • x ~ sqrt(6.2x10^-10 x 0.500) = 1.76x10^-5 M
  • pH = -log(1.76x10^-5) = 4.75
✓ pH = 4.75
Example 3
Hypochlorous Acid

0.050 M HOCl, Ka = 3.0x10^-8.

  • x^2/0.050 = 3.0x10^-8 (approx since Ka << C)
  • x = sqrt(1.5x10^-9) = 3.87x10^-5
  • pH = -log(3.87x10^-5) = 4.41
✓ pH = 4.41

Real-World Applications

🧪
Food Chemistry
Acetic acid in vinegar (~0.8 M): pH ~2.5. Lemon juice (citric acid): pH 2-3.
💧
Natural Waters
Carbon dioxide in water: H2CO3, pKa=6.35. Ocean pH = 8.1 due to carbonate equilibrium.
💊
Drug pH
Aspirin (pKa=3.5) in stomach (pH 2): mostly undissociated, absorbed easily.
🧺
Cleaning Products
Citric acid, acetic acid in household cleaners. pH determines reactivity with mineral deposits.

Common Mistakes to Avoid

⚠️
Use quadratic formula for accuracy

x = (-Ka + sqrt(Ka^2 + 4*Ka*C)) / 2. The simplified x = sqrt(Ka*C) is only valid if x < 5% of C.

⚠️
Check: x must be less than C

If x > C from quadratic, recheck Ka and C values. x is [H+] which cannot exceed initial acid concentration.

⚠️
Strong vs weak acid calculation

Never use pH = -log(C) for weak acids. HF (Ka = 6.8x10^-4) at 0.1 M: pH = 2.08, not 1.00.

Frequently Asked Questions

What is the 5% rule for weak acids? ▾
If percent dissociation < 5%: simplify x^2/C = Ka. Check: x = sqrt(Ka*C). If x/C < 0.05: approximation valid. If not: use quadratic.
How does dilution affect weak acid pH? ▾
Diluting weak acid: pH increases (less acidic) but percent dissociation increases. Double dilution: pH increases by less than 0.30 (unlike strong acids).
What is the pH of a weak acid at half-equivalence point? ▾
In a titration, at half-equivalence: moles acid = moles conjugate base. pH = pKa (Henderson-Hasselbalch with ratio = 1).
Why is HF considered weak despite low pKa? ▾
HF pKa = 3.17. Partial dissociation makes it weak. F- forms strong H-bonds with HF (HF2- ion), complicating behavior. Still a weak acid by definition.
What are some very weak acids? ▾
HCN: pKa=9.21. Phenol: pKa=10.0. Water: pKa=15.7. Ethanol: pKa=16.0. Ammonia: pKa=38 (essentially no acid behavior).

Related Chemistry Calculators

🔬 Strong Acid pH🔬 pH Calculator🔬 Ka Calculator🧪 Henderson-Hasselbalch🔬 Titration

Formula Explorer connections

Interpretation: This relationship connects hydrogen-ion activity, dissociation, conjugate ratios or titration stoichiometry to acid–base behavior. Assumption: Concentration approximates activity mainly in dilute solutions. Temperature, ionic strength, acid strength and equilibrium approximations affect accuracy.

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